Potential energy can be defined as the capacity for doing work which arises from position or configuration. In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges. Charged particles have energy due to their positions. For example, if a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge q in the vicinity of this source charge will be:

U=kQq/r

where k is Coulomb's constant and r is the distance separating the charges.  Note that energy is a scalar, not a vector. To find the total electric potential energy associated with a set of charges, simply add up the energy (which may be positive or negative) associated with each pair of charges.

In electricity, it is usually more convenient to use the electric potential energy per unit charge, just called electric potential or voltage.

Sources

• Department of Physics, Boston University, Lecture Notes, PY106: Elementary Physics II, Accessed 24 March 2010.
• Nave, Carl R., Hyperphysics, Department of Physics and Astronomy, Georgia State University, Accessed 18 August 2008.